D600 vs d7100

It depends how you want to shoot and your reasons for choosing a DSLR. Will you be using the camera in Auto mode usually and letting the camera make decisions? Are you already familiar with how DSLRs work, the different modes, specifically A mode?

If you honestly don't see yourself going beyond Auto mode, I would go with the D7100 (or a lower spec'd model).

If you do plan on using A mode and your primary interest is nice pix of your child with creamy smooth unfocussed backgrounds, the D600 would be the best choice, so long as you could afford a good fast lens. If possible, I'd purchase the 85F1.8 with it and you'd have an extremely-capable, child-portrait/candid combination that would produce a shallower depth of field than any comparable lens on the D7100.

They are both excellent cameras and you can't really go wrong, but the main issue is your budget. Better lenses is where you should be spending your money. If the D600 taps you out and you'd be shooting primarily with the 25-85 kit (which is a good lens), I'd buy the D7100 with a Sigma 50/1.4(or the Nikon 50/1.4) and a Nikon 28/1.8 for less than the D600 kit. Shooting fast primes on the D7100 will produce better child portraits with nice smooth unfocussed backgrounds, better than using the kit lens on the D600.